Question
A car starts from rest and accelerates uniformly at for seconds. Without writing the full equations, find the distance covered using a speed trick suitable for JEE/NEET MCQs.
Solution — Step by Step
Whenever the body starts from rest with uniform acceleration, the distance in time is simply half the area of the velocity-time triangle. We don’t need if we can read the geometry.
. This is the height of the triangle.
. Same answer in one line.
Final answer: .
Why This Works
Kinematics MCQs reward students who treat velocity-time graphs as the primary tool. Once you internalise that the area under a - graph is displacement and the slope is acceleration, problems collapse from three lines of algebra into one geometric step.
For JEE Main and NEET, almost every “from rest” question is a triangle. Every “constant velocity throw” question is a rectangle. Mixed motions become trapeziums. The trick is pattern recognition before formula recall.
Alternative Method
Use Galileo’s odd-number rule: for uniform acceleration from rest, the distances in the 1st, 2nd, 3rd… seconds are in the ratio . Sum of first 5 odd numbers is 25. With , total .
For “ratio of distances” PYQs, jump straight to the odd-number rule. Saves 30 seconds per question.
Common Mistake
Students plug into and waste 20 seconds simplifying. When you see “starts from rest”, skip entirely and write in one stroke.